We investigate spatial interference statistics for multiGigabit outdoor mesh networks operating in the unlicensed 60 GHz millimeter (mm) wave band. The links in such networks are highly directional: because of the small carrier wavelength (an order of magnitude smaller than those for existing cellular and wireless local area networks), narrow beams are essential for overcoming higher path loss, and can be implemented using compact electronically steerable antenna arrays. Directionality drastically reduces interference, but it also leads to deafness making implicit coordination using carrier sense infeasible. In this paper, we make a quantitative case for rethinking medium access control (MAC) design in such settings: unlike existing MAC protocols for omnidirectional networks, where the focus is on interference management, we contend that MAC design for 60 GHz mesh networks can essentially ignore interference, and must focus instead on the challenge of scheduling half-duplex transmissions with deaf neighbors. Our main contribution is an analytical framework for estimating the collision probability in such networks, as a function of the antenna patterns and the density of simultaneously transmitting nodes. The numerical results from our interference analysis show that highly directional links can indeed be modeled as pseudowired, in that the collision probability is small even with a significant density of transmitters. Furthermore, simulation of a rudimentary directional slotted Aloha protocol shows that packet losses due to failed coordination are an order of magnitude higher than those due to collisions confirming our analytical results and highlighting the need for more sophisticated coordination mechanisms.